Robust constraint satisfaction: invariant sets and predictive control

Set invariance plays a fundamental role in the design of control systems for constrained systems sincethe constraints can be satisfied for all time if and only if the initial state is contained inside an invariantset. This thesis is concerned with robust set invariance theory and its application to guaranteeingfeasibility in model predictive control.In the first part of this thesis, some of the main ideas in set invariance theory are brought togetherand placed in a general, nonlinear setting. The key ingredients in computing robust controllable andinvariant sets are identified and discussed. Following this, linear systems with parametric uncertaintyand state disturbances are considered and algorithms for computing the respective robust controllableand invariant sets are described. In addition to discussing linear systems, an algorithm for computingthe robust controllable sets for piecewise affine systems with state disturbances is described.In the second part, the ideas from set invariance are applied to the problem of guaranteeing feasibilityand robust constraint satisfaction in Model Predictive Control (MPC). A new sufficient condition isderived for guaranteeing feasibility of a given MPC scheme. The effect of the choice of horizons andconstraints on the feasible set of the MPC controller is also investigated. Following this, a necessaryand sufficient condition is derived for determining whether a given MPC controller is robustly feasible.The use of a robustness constraint for designing robust MPC controllers is discussed and it is shownhow this proposed scheme can be used to guarantee robust constraint satisfaction for linear systemswith parametric uncertainty and state disturbances. A new necessary and sufficient condition as wellas some new sufficient conditions are derived for guaranteeing that the proposed MPC scheme isrobustly feasible.The third part of this thesis is concerned with recovering from constraint violations. An algorithm ispresented for designing soft-constrained MPC controllers which guarantee constraint satisfaction, ifpossible. Finally, a mixed-integer programming approach is described for finding a solution whichminimises the number of violations in a set of prioritised constraints

Distributed Model Predictive Control for Reconfigurable Large-Scale Systems

Large-scale Systems are gaining more importance in the modern world requiring flexible techniques capable of handling interactions. This thesis is concerned with the development of suitable algorithms based on Model Predictive Control (MPC) that guarantee stability, recursive feasibility and constraint satisfaction. In the first part of this thesis, the main properties and control challenges for controlling an Large-Scale System are brought together, and the main distributed approaches for solving these problems are surveyed. Also, two novel Distributed MPC algorithms are presented. A non-centralised approach to the output-feedback variant of tube-based model predictive control of dynamically coupled linear time-invariant systems with shared constraints. A tube-based algorithm capable of handling the interactions–not rejecting them– that replaces the conventional linear disturbance rejection controller with a second MPC controller, as is done in tube-based nonlinear MPC. Following this, a smart-grids application of the developed algorithm is presented to solve the load frequency control for a power network. The approach achieves guaranteed constraint satisfaction, the recursive feasibility of the MPC problems and stability while maintaining on-line complexity similar to conventional MPC. The second part of the thesis covers reconfigurable distributed MPC. Two novel approaches are considered: a nominal MPC methodology that incorporates information of external disturbances, and a coalitional approach for robust distributed MPC. The first approach uses available disturbance predictions within a nominal model predictive control formulation is studied. The main challenge that arises is the loss of recursive feasibility and stability guarantees when a disturbance, which may change from time step to time step, is resent in the model and on the system. We show how standard stabilising terminal conditions may be modified to account for the use of disturbances in the prediction model. Robust stability and feasibility are established under the assumption that the disturbance change across sampling instances is limited. The proposed coalitional approach to robust Distributed MPC aims to tackle the existing trade-off between communication and performance in Large-Scale System by exploiting the different network topologies of system dynamics. The algorithm employs a method to switch between topologies using a multi-rate control approach. The optimal topology selection problem is solved using a consensus approach appropriately constrained to reduce the effects of any combinatorial explosion. The robust control algorithm is capable of recomputing the necessary parameters online to readjust to new partitions. Robust constraint satisfaction, recursive and stability are guaranteed by the proposed algorithm

Advanced control for miniature helicopters : modelling, design and flight test

Unmanned aerial vehicles (UAV) have been receiving unprecedented development during the past two decades. Among different types of UAVs, unmanned helicopters exhibit promising features gained from vertical-takeoff-and-landing, which make them as a versatile platform for both military and civil applications. The work reported in this thesis aims to apply advanced control techniques, in particular model predictive control (MPC), to an autonomous helicopter in order to enhance its performance and capability. First, a rapid prototyping testbed is developed to enable indoor flight testing for miniature helicopters. This testbed is able to simultaneously observe the flight state, carry out complicated algorithms and realtime control of helicopters all in a Matlab/Simulink environment, which provides a streamline process from algorithm development, simulation to flight tests. Next, the modelling and system identification for small-scale helicopters are studied. A parametric model is developed and the unknown parameters are estimated through the designed identification process. After a mathematical model of the selected helicopter is available, three MPC based control algorithms are developed focusing on different aspects in the operation of autonomous helicopters. The first algorithm is a nonlinear MPC framework. A piecewise constant scheme is used in the MPC formulation to reduce the intensive computation load. A two-level framework is suggested where the nonlinear MPC is combined with a low-level linear controller to allow its application on the systems with fast dynamics. The second algorithm solves the local path planning and the successive tracking control by using nonlinear and linear MPC, respectively. The kinematics and obstacle information are incorporated in the path planning, and the linear dynamics are used to design a flight controller. A guidance compensator dynamically links the path planner and flight controller. The third algorithm focuses on the further reduction of computational load in a MPC scheme and the trajectory tracking control in the presence of uncertainties and disturbances. An explicit nonlinear MPC is developed for helicopters to avoid online optimisation, which is then integrated with a nonlinear disturbance observer to significantly improve its robustness and disturbance attenuation. All these algorithms have been verified by flight tests for autonomous helicopters in the dedicated rapid prototyping testbed developed in this thesis.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Verification of advanced controllers for safety-critical systems

In order to design and deploy a feedback controller in a real application, one must determine suitable specifications that the design must meet ("validate"), and then ensure that the chosen specifications have been met ("verify"). In this thesis, we investigate a verification paradigm based on formal methods, such as the Satisfiability Modulo Theories (SMT) and quantifier elimination (Weispfenning’s virtual term substitution and quantifier elimination by cylindrical algebraic decomposition) algorithms. Any control design requirement (such as satisfactory performance, robustness to uncertainties, stability, etc.) that can be expressed in a first order logic formula can be (in principle) verified by using one of these methods. Consequently, in principle, this allows us to consider problems like general non-convex optimisation, exact computation of structured singular value, and synthesis of non-convex feasible parameter sets. In practice, the generality of algorithms like quantifier elimination by cylindrical algebraic decomposition come with a downside of high running time when applied to more complex systems with more parameters. This, in some cases, limits the complexity of the system that we could consider. Therefore, we focused our attention on control problems such as obtaining an explicit MPC law for a linear time invariant system with a quadratic objective and polytopic constraints, or computation of the structured singular value for a system under parametric (and not norm-bounded) uncertainty. Such problems can be expressed as quantifier elimination problems with a particular quantification structure that allows us to take advantage of a specialised quantifier elimination algorithm - the quantifier elimination by Weispfenning’s virtual term substitution procedure that has much lower worst-case running time on these types of problems than quantifier elimination by cylindrical algebraic decomposition algorithm. Despite these constraints, we were able to apply a quantifier-elimination-based verification framework to clearance of a flight control law developed for a real world industrial system from the aerospace field not only at particular combination of parameters but throughout the whole flight envelope. In conclusion, while in principle formal methods are applicable to a large body of problems arising in control theory, more widespread practical application depends on further research in efficiency and running time improvement in the implementation of these algorithms.Full EC Project Title: Reconfiguration of control in flight for integral global upset recovery (RECONFIGURE) EC Project #: 314544 RG # & UFS Project Code: RG66745, NMZN/04

Measurements, Models, Systems and Design

531 s.

Real-Time Sensor Networks and Systems for the Industrial IoT

The Industrial Internet of Things (Industrial IoT—IIoT) has emerged as the core construct behind the various cyber-physical systems constituting a principal dimension of the fourth Industrial Revolution. While initially born as the concept behind specific industrial applications of generic IoT technologies, for the optimization of operational efficiency in automation and control, it quickly enabled the achievement of the total convergence of Operational (OT) and Information Technologies (IT). The IIoT has now surpassed the traditional borders of automation and control functions in the process and manufacturing industry, shifting towards a wider domain of functions and industries, embraced under the dominant global initiatives and architectural frameworks of Industry 4.0 (or Industrie 4.0) in Germany, Industrial Internet in the US, Society 5.0 in Japan, and Made-in-China 2025 in China. As real-time embedded systems are quickly achieving ubiquity in everyday life and in industrial environments, and many processes already depend on real-time cyber-physical systems and embedded sensors, the integration of IoT with cognitive computing and real-time data exchange is essential for real-time analytics and realization of digital twins in smart environments and services under the various frameworks’ provisions. In this context, real-time sensor networks and systems for the Industrial IoT encompass multiple technologies and raise significant design, optimization, integration and exploitation challenges. The ten articles in this Special Issue describe advances in real-time sensor networks and systems that are significant enablers of the Industrial IoT paradigm. In the relevant landscape, the domain of wireless networking technologies is centrally positioned, as expected